following from: https://sketchucation.com/forums/viewtopic.php?f=323&t=68433&p=626632#p626632
I took some time to explain why I think adding a "preserve quads" method could make sense to have in both JPP and NPP. I added in attachment the example .skp, in case this can be helpful.
I suppose there are quite a lot of people out there that uses JPP in combination with quad-friendly tools (Sub-d, QFT, VT, Curviloft, TIG extrude, Trupaint, and so on..)
I'm curious if someone else has encountered similar problems and if, maybe they found better/alternative/faster workarounds for theese situations.
I've created a basic quad topolgy example, in which I extrude a faceloop with Regular JPP (both with borders = "contours" and border = "each face") and Normal JPP, to show you when it would make sense to have a "preserve quads" option.
QuadFaceTools live mesh analysis is activated, so you can see that when quad (not shadow casting) diagonals are present, all the three methods produces triangles instead of preserving the "diagonal" behaviour.
Below you can see why this is not ideal for subdivision, as the triangles produces bad topology and smoothing artifacts.
Here you can see an orthographic top view of the same stuff, with monocrome style and edge visibility turned off, to emphatyze the smoothing artifacts.
With normal push pull you got an option to keep triangles, but still that doesn't preserve the "do not cast shadow" property, so that, even if the artifacts are less evident than the other methods, you can tell that the topology is slightly distorted. It's rather easy to fix this manually, just filtering selection for smooth edge (i use TT selection toys in order to do this quickly) then i check/uncheck smooth-soft/cast shadow in "entity info" dialog.
As you previously said, hopefully this is a rather simple (but effective) option to add, in order to automate the cleanup.
What I'm not sure is easy to fix at all, would be the quad-managing behaviour of regular JPP, as you can see below, there are a few more problems, with both methods.
"Create borders for each face" also produces inner faces, wich completely screw the subdivisions.
Notice that in addition to smoothing artifacts, you get messed UV, due to the topology distorsion and the presence of triangles would cause, for instance, Trupaint "quad" method to fail.
Moreover selection of rings/loop is screwed and you'll have problems if you need to do furter modifications to the mesh or manually unwrap it, and so on..
What I've found that DOES preserve the diagonals (at least in my experience) is regular JPP with "No Borders" option ticked.
Unfortunately, as you can see, it destroyes the surronding edges, so that some faces are lost.
Nevertheless, i think this method, is the best starting point for my manual workaround, which I'll try my best to show you, hoping that there's some little chance to automate/incorporate it in future developements of JPP.
The fact wich gives me some sort of hope, is that I use your brilliant Curvyloft to fix this, so maybe you could integrate some code from that.
Let's start with fresh geometry: to prevent missing faces, I select the geometry I need to JPP->invert selection->include inner (hole) loop in selection!!->make first group.
Triple click the remaining loose geometry and make a second group.
Perform JPP "No Tickening - No Borders" (diagonals preserved-live mesh analysis ok!)
Select both groups->explode
Pick the outer loops and run regular curviloft (lowered from default 5 segments to only 1 segment)
Do exactly the same for inner loops
Final cleanup: Select both curviloft groups->explode->orient faces->run ThomThom QFT"UnsmoothQuads"
Not sure it easy/possible to replicate such operation in JPP but that would be a MAJOR improvement to the usability of JPP in organic/subdivision modelling.
But if it's not possible we have to tank you anyway because, as you can see, with some minor tricks and workarounds JPP and Curviloft togheter have tons of usefulness in this kind of modelling! 
JPPquadExample.skp
